n-adic means for various distributions

distributions.py

# histograms of various distributions

import numpy as np

import matplotlib.pyplot as plt
import matplotlib as mpl
mpl.rcParams['mathtext.fontset'] = 'cm'

normal_50 = np.random.normal(50, scale=13, size=100000)
normal_30 = np.random.normal(30, scale=10, size=100000)
normal_70 = np.random.normal(70, scale=10, size=100000)
exponential = np.random.exponential(scale=12, size=100000)
gumbel = np.random.gumbel(loc=20, scale=8, size=100000)
uniform = np.random.uniform(0, 100, size=100000)

samples = [
    (normal_30, 'normal $\mu=30$'),
    (normal_50, 'normal $\mu=50$'),
    (normal_70, 'normal $\mu=70$'),
    (exponential, 'exponential'),
    (gumbel, 'gumbel'),
    (uniform, 'uniform')
]

for sample, _ in samples:
    sample = [s for s in sample if 0 <= s <= 100]
    plt.hist(sample, histtype='step', bins=1000)

plt.legend([sample[1] for sample in samples])
plt.title('Distributions')
plt.yticks(range(0, 101, 10))
plt.show()

power_means.py

# n-adic mean simulation

import numpy as np

import sys

import matplotlib.pyplot as plt
import matplotlib as mpl
mpl.rcParams['mathtext.fontset'] = 'cm'

normal_50 = np.random.normal(50, scale=13, size=10000)
normal_30 = np.random.normal(30, scale=10, size=10000)
normal_70 = np.random.normal(70, scale=10, size=10000)
exponential = np.random.exponential(scale=12, size=10000)
gumbel = np.random.gumbel(loc=20, scale=8, size=10000)
uniform = np.random.uniform(0, 100, size=10000)

def mean(lst,p=1):
    return (sum(x**p for x in lst) / len(lst))**(1/p)

def power_means(sample):
    plt.plot([mean(sample, p) for p in range(1,200)])
    plt.xlabel('$p$')

samples = [
    (normal_30, 'normal $\mu=30$'),
    (normal_50, 'normal $\mu=50$'),
    (normal_70, 'normal $\mu=70$'),
    (exponential, 'exponential'),
    (gumbel, 'gumbel'),
    (uniform, 'uniform')
]

for sample, _ in samples:
    sample = [s for s in sample if 0 <= s <= 100]
    power_means(sample)

plt.legend([sample[1] for sample in samples])
plt.title('Power means')
plt.yticks(range(0, 101, 10))
plt.show()

Simple uniform n-adic means, for p between 0 and 150

Distribution histograms

Power means for each of the above distributions